Robust Tucker Tensor Decomposition for Effective Image Representation

Many tensor based algorithms have been proposed for the study of high dimensional data in a large variety of computer vision and machine learning applications. However, most of the existing tensor analysis approaches are based on Frobenius norm, which makes them sensitive to outliers, because they minimize the sum of squared errors and enlarge the influence of both outliers and large feature noises. In this paper, we propose a robust Tucker tensor decomposition model (RTD) to suppress the influence of outliers, which uses L₁-norm loss function. Yet, the optimization on L1-norm based tensor analysis is much harder than standard tensor decomposition. In this paper, we propose a simple and efficient algorithm to solve our RTD model. Moreover, tensor factorization-based image storage needs much less space than PCA based methods. We carry out extensive experiments to evaluate the proposed algorithm, and verify the robustness against image occlusions. Both numerical and visual results show that our RTD model is consistently better against the existence of outliers than previous tensor and PCA methods.